DiophantineEquation.cpp

#include <iostream>
#include <cmath>
#include <string>
#include <vector>
#include <string_view>
using namespace std;
class Dioph {
public:
    static vector<pair<long, long>> solEquaStr(long long n) {
        vector<pair<long, long>> results;
        for (long long a = 1; a * a <= n; ++a) {
            if (n % a == 0) {
                long long b = n / a;
                if ((a + b) % 2 == 0 && (b - a) % 4 == 0) {
                    long long x = (a + b) / 2;
                    long long y = (b - a) / 4;
                    results.push_back({ x, y });
                }
            }
        }
        return results;
    }
};
int main()
{
    vector<pair<long, long>> result1 = Dioph::solEquaStr(90005);
}
/*Description:

In mathematics, a Diophantine equation is a polynomial equation, usually with two or more unknowns,
such that only the integer solutions are sought or studied.

In this kata we want to find all integers x, y (x >= 0, y >= 0) solutions of a diophantine equation of the form:
x2 - 4 * y2 = n

(where the unknowns are x and y, and n is a given positive number) in decreasing order of the positive xi.

If there is no solution return [] or "[]" or "". (See "RUN SAMPLE TESTS" for examples of returns).
Examples:

solEquaStr(90005) --> "[[45003, 22501], [9003, 4499], [981, 467], [309, 37]]"
solEquaStr(90002) --> "[]"

Hint:

x2 - 4 * y2 = (x - 2*y) * (x + 2*y)
Fundamentals
Mathematics
Algebra*/
//          ／＞　　フ
//　　　　　| 　n　n 彡
//　 　　　／`ミ＿xノ
//　　 　 /　　　 　 |
//　　　 /　 ヽ　　 ﾉ
//　 　 │　　|　|　|
//　／￣|　　 |　|　|
//　| (￣ヽ＿_ヽ_)__)
//　＼二つ
// ITS CAT FOR YOU